Journal of Thermodynamics

Volume 2015 (2015), Article ID 319704, 8 pages

http://dx.doi.org/10.1155/2015/319704

## Thermodynamic Modeling of Surface Tension of Aqueous Electrolyte Solution by Competitive Adsorption Model

^{1}Department of Chemical Engineering, Islamic Azad University, Bushehr Branch, Bushehr 751961955, Iran^{2}National Iranian Gas Company (NIGC), Fajr-e Jam Gas Company, Bushehr, Iran

Received 14 August 2015; Accepted 4 October 2015

Academic Editor: Marc D. Donohue

Copyright © 2015 Mohamad Javad Kamali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Thermodynamic modeling of surface tension of different electrolyte systems in presence of gas phase is studied. Using the solid-liquid equilibrium, Langmuir gas-solid adsorption, and ENRTL activity coefficient model, the surface tension of electrolyte solutions is calculated. The new model has two adjustable parameters which could be determined by fitting the experimental surface tension of binary aqueous electrolyte solution in single temperature. Then the values of surface tension for other temperatures in binary and ternary system of aqueous electrolyte solution are predicted. The average absolute deviations for calculation of surface tension of binary and mixed electrolyte systems by new model are 1.98 and 1.70%, respectively.

#### 1. Introduction

For studying the aqueous electrolyte solution in porous media, distillation, extraction process, and liquid-liquid dispersion, the calculation of surface tension of aqueous solutions is required [1]. So different equations have been developed to calculate surface tension of mineral salts. Ariyama [2], Lorenz [3], Young and Grinstead [4], and Gleim and Shelomov [5] formulated useful equations as group contribution method for calculation of surface tension of some limited binary electrolyte-water systems. Oka [6] proposed an equation for calculation of surface tension based on the concentration of solution, electronic charge, dielectric constant of water, ionic charge, and Avogadro’s constant. Later Hovarth [7] developed this equation by introducing the ionic strength and degree of dissociation into Oka’s model [6]. Onsager and Samaras [8] obtained a relation based on the temperature, dielectric constant of water, and concentration of solution for calculation of surface tension of electrolyte solution. Schmutzer [9] considered the osmotic coefficient as an important factor for calculation of surface tension of electrolyte solution. Adding a proportional factor of anion concentration to the surface tension of water, the surface tension of aqueous electrolyte solution was determined by Abramazon and Gaukhberg [10]. This parameter was considered as a function of the inverse of square of ionic radius and anion charge. Li et al. [1] developed a new model for calculation of surface tension of single and mixed electrolyte solution. In this model, the surface layer is considered as a distinct phase where the electrolytes could be entered into it from other phases. The surface tension was obtained using the proportion of molality of salt in surface layer to liquid bulk phase. While this model had satisfactory results in low concentration of electrolytes, in high concentration the calculated surface tension was not in good agreement with experimental data. Yu et al. [11] combined Li et al. [1] model with modified mean spherical approximation (MSA) as osmotic coefficient model. The results showed that the calculated surface tension in highly concentrated regions was improved. Furthermore, the Langmuir gas-solid adsorption model was used at equilibrium condition for calculation of surface tension of mineral salts by Li and Lu [12]. The results indicated the satisfactory agreement with experimental data. Sadeghi et al. [13] used the combination of MSA model [14] with the Ghotbi and Vera [15] and the Mansoori et al. [16] equations of state, for correlation of the surface tension of single aqueous solution. Also the surface tension of different mixed aqueous solutions was predicted by this approach. The results indicate the satisfactory agreement between calculated and experimental data [13].

In this paper, a new model for calculation of surface tension of the electrolyte systems is developed using the Langmuir adsorption equation and E-NRTL [17] model. The adjustable parameters of this model are obtained by experimental data of surface tension at single temperature. Then the model is verified by prediction of surface tension of 65 binary electrolyte-water systems and 17 ternary electrolyte systems.

#### 2. Thermodynamic Modeling

For calculation of surface tension of electrolyte system, the aqueous electrolyte solution-vapor system is supposed as three different phases: bulk vapor phase, surface phase, and bulk liquid phase (Figure 1). The surface phase is considered as distinct layer for adsorption of electrolyte from liquid phase. In this system, the chemical potential of water in liquid bulk phase and surface would be defined as follows [1]:where , , , and represent the chemical potential, activity, partial molar area, and surface tension of solution. The subscripts , , , , and refer to water, liquid phase, surface phase, reference state of liquid phase, and reference state of surface phase, respectively.